Valorization of ancillary services for the voltage control in a distribution network

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OFFICIAL'MASTER'S'DEGREE'IN'THE'

'ELECTRIC'POWER'INDUSTRY'

'

Master’s'Thesis'

' ' ' ' '

Valorization of Ancillary Services for The

Voltage Control in a Distribution Network

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' '

!

Author:! Yen,Chun!Chou!

Supervisor:! Prof.!Marc!Petit!! Co,!Supervisor:!!!!!!!!!!!!!!!!!!!!!Dr.!Yannick!Perez! Madrid,!!!07!2015!

UNIVERSIDAD'PONTIFICIA'COMILLAS'

'

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Official!Master's!Degree!in!the!Electric!Power!Industry!(MEPI)!

Erasmus!Mundus!Joint!Master!in!Economics!and!Management!of!Network!Industries!(EMIN)! !

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$ $

Master’s$Thesis$Presentation$Authorization$

!

THE!STUDENT:!

YenRChun!Chou!

! !

……….!

! !

!

THE!SUPERVISOR!

Prof.!Marc!Petit,!CentraleRSupelec!!

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Signed:!!………!!!!!!!!!!!!!!Date:!……/!……/!……!

!

THE!CORSUPERVISOR!

Dr.!Yannick!Perez!

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Signed:!!………..…!!!!!!!!!!!!!!Date:!……/!……/!……!

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Authorization!of!the!Master’s!Thesis!Coordinator!

Dr.!Javier!García!González!

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Signed:!!………!!!!!!!!!!!!!!Date:!……/!……/!……!

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RASMUS'

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UNDUS'

J

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ASTER'IN'

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CONOMICS'

AND'

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ANAGEMENT'OF'

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ETWORK'

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NDUSTRIES'

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Master’s'Thesis'

' ' ' ' '

Valorization of Ancillary Services for The

Voltage Control in a Distribution Network

' ' ' ' ' ' ' ' ' '

' ' !

Author:! Yen,Chun!Chou!

Supervisor:! Prof.!Marc!Petit!!

Co,!Supervisor:!!!!!!!!!!!!!!!!!!!!!Dr.!Yannick!Perez! Madrid,!!!07!2015!

UNIVERSIDAD'PONTIFICIA'COMILLAS'

'

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Summary

The distribution grid and distribution system operators (DSOs) are facing a great challenge because of new the technologies, such as plug-in electric vehicles, demand response (DR), and distributed generations (DG). These technologies change the system voltage profile and impact the grid operation. Initially, the DSOs activities are related to grid reinforcement and maintenance. Presently, the unexpected and/or unpredicted power injection totally modifies the voltage profile. The power flow is no longer unidirectional and the consumption loads are no longer inflexible. To adapt to this change, there are two prevalent ways: a) using ancillary services and b) reinforcing system grid. Unfortunately, ancillary services haven’t fully been introduced into the distribution system.

In order to introduce ancillary services into the distribution system, I include DSOs preferences into voltage control cost function. Therefore, depending on DSOs preferences, the usage of each resource will be different. This can promote the development of distribution ancillary services without disturbing the market. The result shows that using ancillary services can help to postpone the grid reinforcement plan up to 23 years in a specific system, and the cost voltage control is lower than the cost of grid reinforcement. However, the system reinforcement cannot be avoided if the demand keeps growing. The result also shows that even with different preferences, the effects of using ancillary services are the same, but the costs of voltage control are different.

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Acknowledgements

It’s my pleasure to thank those who have contributed in, if I may say it myself, the successful completion of the thesis. First, my special appreciation goes to Yannich Perez for giving me this opportunity to develop my thesis in Supelec. Second, I would like to forward my mega gratitude to my supervisor Marc Petit for his kindness and patience. My thesis journey would not have been manageable without your help and you are truly a knowledgeable and patient professor. Equally important, Supelec

energy department staff members should be acknowledged. Without your advices and guidance, I would not be able to achieve what I have accomplished. Last but not least, to all the professors in Comillas, Paris-sud 11, and Supelec, a big thank you to all of you and God bless you.

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TABLE&OF&CONTENTS&

Summary!...!iii!

Acknowledgements...!iv!

Table!of!Contents...!v! ! !

List!of!Figures...!vii! !

List!of!Tables!...!ix!

Chapter!1! Introduction!...!1!

Chapter!2! Literature!Review!and!Problem!Setting...!3! !

2.1!Ancillary!services...!3! !

2.2!Ancillary!services!remunerations...!4!

2.2.1!MarketHbased...!4!

2.2.2!CostHbased!...!5!

2.2.3!ReaHtime!based...!5!

2.2.4!Zonal!pricing...!6!

2.2.5!Nodal!pricing!...!8!

2.3!Smart!gird!...!11!

2.4!Demand!response!...!13!

2.4.1 Contracted-based...!14!

2.4.2 Market-based...!14!

2.4.3 Real-time based...!15!

2.5!Operating!methodologies...!15!

Chapter!3! Methodology!...!19! !

3.1!Distribution!generation!...!19!

3.2!Demand!response!...!20!

3.3!Gird!reinforcement!...!20!

3.4!Model!setting...!20!

3.4.1!Cost!of!OLTC...!21!

3.4.2 Cost of using DG...!22

3.4.3 Cost of reactive power...!22

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!

Chapter!4!

Results...!25!

4.1 Base case: OLTC!...!25

4.2!Case 1: OLTC& ancillary services!...!28!

4.3 Case 2: OLTC, DR, and ancillary service ...!29

4.4 Case 3: OLTC, DR, and ancillary service...!31!

4.5 Case 4: Grid reinforcement...!32

4.6 Economic analysis...!36

! Chapter!5! Conclusions!...!41! !

! Bibliography...!43!

Appendix!A!H!Market spot price!...!45! !

Appendix!B!–!PVIFA!...!57! !

Appendix!C!–!Growth!results!...!59! !

! ! ! ! ! ! ! ! ! ! ! ! ! ! !

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List&of&Figures&

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Figure!1!H!26th_!_{Reactive Market Report} Figure 2 - Lost Opportunity Cost

Figure 3 - An example of generator’s active power losses as a function of produced reactive power at rated MW output

Figure!4!–!EU!20H20H20!plan!

Figure!5!H!Operation!state!of!TCL!appliance

Figure!6!H!Priority!queue!structure!with!TCL!units! Figure!7!HTCL!control!processes

Figure!8!–!Modified!IEEE!34Hnode!model! Figure!9!–!Demand!Response!prices!and!hours Figure 10 – DSO preference

Figure 11 –Load profile and based case voltage profile!

Figure 12 – Bus 35 voltage profile Figure 13 - Bus 23 voltage profile Figure 14 – Bus 34 voltage profile Figure 15 – Bus 34 voltage profile

Figure 16 – Case 1 voltage profile and cost Figure 17– Case 1 bus 35 voltage profile Figure 18– Case 1 bus 23 voltage profile Figure 19– Case 2 voltage profile and cost Figure 20 – Case 2 bus 35 voltage profile Figure 21 – Case 2 bus 23 voltage profile Figure 22 – Case 3 voltage profile and cost Figure 23 – Case 3 bus 35 voltage profile Figure 24 – Case 3 bus 23 voltage profile Figure 25 – Case 4 voltage profile

Figure 26 – Voltage violations Figure 27 – Cost comparison 1 Figure 28 – Cost comparison 2 Figure 29 – preference comparison

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Figure 30 – Cost comparison 3 Figure 31 – Cost comparison 4

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&

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List&of&Tables&

Table!1H!Revenue!requirement!

Table 2- Smart grid services

Table 3- Smart grid issues!

Table 4 - Cost of Wind in France Table 5 – Lines information

Table!6!–!Cost!of!grid!reinforcement!

Table 7 – 3-year plan with high cost Table 8 – 3-year plan with low cost Table 9 - 5-year plan with high cost Table 10 - 5-year plan with low cost

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CHAPTER 1 Introduction

The distribution grid and distribution system operators (DSOs) are facing a great challenge because of new technologies, such as plug-in electric vehicles, demand response (DR), and distributed generations (DG). These technologies change the system voltage profile and impact grid operating. Initially, the distribution system is designed with a simple radial structure, through which loads are connected to a main feeder. Under this structure, the system control is relatively simple, so most of the DSOs activities are related to grid reinforcement and maintenance. Before those new technologies, in the distribution system, the voltage level decreased along the feeders due to the load consumption. In other words, the closer a substation is to the feeders, the higher the voltage level it gets. Presently, the system voltage profile has been modified because of the DG power injection, such as wind, solar, and so forth. The unexpected and/or unpredicted power injection totally modifies the voltage profile. To adapt to this change, there are two prevalent ways: a) using ancillary services and b) reinforcing system grid. The ancillary services are usually acquired through direct contracts and/or market auctions in many deregulated transmission systems. Unfortunately, these services haven’t fully been introduced into the distribution system.

However, the electrical characteristics of distribution grid are different from those of transmission grid. For instance, the line resistance and reactance are different. Because the ratio of R/X in distribution system is greater than in transmission system, any power injection in distribution system will create a greater voltage deviation. Therefore, only using reactive power to compensate voltage peaks is insufficient. DSOs have to use other tools at the same time, such as demand response. Moreover, in order to prevent a dramatic change in renewable power injection, demand-side control plays an important role. Depending on the location and system condition, the required amount of flexibility is different. Nowadays, many of ancillary services in distribution system are not remunerated. However, if many of these system services are paid in transmission level, it should not be a case in distribution.

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Regulation rules and operating approach will also influence DSOs activities. Different regulation policies will have different system approaches, for instance, the system approach can be minimizing system losses, maximizing system security, or minimizing power costs. Different approaches will have different dispatch plans, and one approach may have conflicts with another. For instance, if the system approach is to minimize losses, it might accept an expensive offer provided by the supplier locating close to the demand. Another example of this is that if the system approach is to minimize power costs, it might choose a low-priced offer provided by a far-off generator, which will increase system losses. Operating methodology also has to improve due to the new technologies. The power flow is no longer unidirectional and the consumption loads are no longer inflexible. DSOs operating methodologies have to switch to a real-time operation.

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CHAPTER 2 Literature review and problem setting

2.1 Ancillary services

According to the Agency of Cooperation of Energy Regulators (ACER), Ancillary Services are “services necessary to support transmission of electric power between generation and load, maintaining a satisfactory level of operational security and with a satisfactory quality of supply. The main elements of ancillary services include active and reactive power reserves for balancing power and voltage control. Active power reserves include automatically and manually activated reserves and are used to achieve instantaneous physical balance between generation and demand. Further elements of ancillary services may include black start, inertial response, trip to house-load, spinning reserve and islanding capability. In the liberalized market, many ancillary services are contracted by Transmission System Operators from selected grid users that qualify for providing these services” (ACER 2011). In other words, there are three categories of ancillary services, which are voltage control, frequency control, and operating reserves, and two main elements to the services, which are active and reactive power.

In voltage control, not only active power but also reactive power plays an important role. For instance, operators can use reactive power to compensate voltage drops. Because the reactive power losses is high, so the reactive power inject, or the provide point, must be as close to the target point as possible. There are some other tools to control the voltage as well, such as transformer tap changers and voltage regulators.

For frequency control, system operators have to maintain the grid frequency within the specific boundaries. The imbalances between the supply and demand will cause frequency variations. A significant frequency variation may cause a power failure. Usually generators are required to provide frequency control through automatic generation control (AGC).

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Having operating reserves allows system operators to solve any system imbalance. Traditionally, generators offer balancing reserves, and the reserves can be further divided into many different categories, such as primary, secondary, and tertiary reserve. Operating reserves can be upward or downward reserves. In other words, operating reserves can be a reserve to increase or decrease power output.

2.2 Ancillary services remunerations

In transmission system, ancillary services are acquired through different methods in different countries.

2.2.1 Market-based

The service is acquired through an auction/tender, and the price could be a unity market price or a pay-as-bid. The criteria for choosing service providers and market clearing methodology depend much on the country and its regulation rules. For example, in United Kingdom (UK), they use auction to acquire the system service. In figure 1, it shows the result of 26th reactive market auction. According to the market criteria, each tender will have a score. If the score is positive, it means that the tender should be offered a market agreement. Likewise, if the score is negative, it means the tender should not be offered a market agreement.

Figure 1 –26th Reactive Market Report

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2.2.2 Cost-Based

The amount of remuneration is based on the cost of services or the revenue requirement. Service providers are required to disclose their cost functions, technique constraints, and other required information to system operator and/or commission.

Table 1 –Revenue requirement

(Source: PJM, 2015)

2.2.3 Real-time based

Based on the system contribution, service providers will receive a different amount of payment. This approach can also be used to compensate the service provider who has to provide extra service in real-time. One way to remunerate the service under this approach is using lost opportunity cost (LOC).

!"#_! =!"# !"#$_!"_,_!×! !"#_! −!!"# !"#_!,!"#_!,!"#_!

−! !"#

!"#!

!"# !"#!,!"#!,!"#!

,0 ×! !!

3600!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(1)!!!!!!!!

Where:

LOCi = Lost Opportunity Cost for interval i;

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EOPi = The Generator’s Economic Operating Point for interval i;

AEIi = The Generator’s Actual Energy Injection for the interval i;

RTSi = The Generator’s Real-Time Energy Schedule for interval i;

DASi = The Generator’s Day-Ahead Schedule for the hour containing i;

Bidi = Generator’s Bid curve in effect for interval i;

Si/3600= The length of interval i, containing Si seconds, in units of hours.

Figure 2 - Lost Opportunity Cost

(Source: PJM, 2013)

2.2.4 Zonal pricing

In "Definition of a Zonal Reactive Power Market Based on the Adoption of a

Hierarchical Voltage Control" (Careri, Genesi, Marannino, Montagna, & Rossi,

2010), the authors presented a zonal pricing approach under hierarchical automatic voltage regulation framework. In the case of Italy, there are three levels of voltage control: a local level (AVR, Automatic Voltage Regulation), a regional secondary level (SVR, Secondary Voltage Regulation) and a national third (TVR, Tertiary Voltage Regulation). First, they divided the distribution network into different zones and then selected a pilot node for each zone. The pilot node must be able to represent the zonal voltage profile. Moreover, some generators will be selected to provide SVR

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in each zone, and these generators must be able to affect the pilot node voltage in the same zone. In this model, pilot nodes are treated as PV buses and those selected generators are treated as PQ buses.

The marginal real power loss variation [MW/Mvar], due to the reactive injection _Qiin

PQ bus i is presented as follows:

!PL

!Qi = !PL

!Qi+ (!k,j !k !!! ∙!Qk,j !Qi !A !!!

)+ (!v,l

!Q

!!!

∙!Vl

!Qi)+ (!Q,P

!v

!!!

∙!Qp

!Qi)!!!!!!!!!!!!!!!!!!!!!(2)

Where:

λk, j _{are associated to alignment constraints;}

λV ,l _{are related to PQ bus voltage constraints;}

λ_Q_,_pare referred to PV capability constraints;

NA is the number of SVR control areas;

mk is the number of controlled generators in SVR area k;

NQ is the number of PV generators;

NV is the number of PQ bus.

Some constraints are considered as hard constraints, which cannot be violated, so the Lagrange multiplier of this type of constraint will be zero. On the other hand, the upper and lower bounds of voltage magnitudes are imposed by the TSO, which are considered as soft constraints. Therefore, by modifying the boundary, these soft constraints can be disregarded. Finally, the nodal margin price is presented as follows:

!_!"#$_,_! = !_!"!∙!!! !!_!!!!

€

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It shows that the price of reactive power is a portion of the active power price, and the ratio is system sensitivity of power losses to reactive power changes.

2.2.5 Nodal pricing

Staniulis (2001) presented a common nodal pricing method in “Reactive Power

Valuation” by using the voltage sensitivity between the generators and loads.

!"#_!" = !"!" !"_!" !

!"

∙!"#_!"!;!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(4)!

!"#_!" = !"!" !"_!" !

!"

∙!"#_!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(5)

QLSLi and PLSLi represent the sensitivity of active power losses to reactive and active

power injection for different buses. !"_!" represents the sensitivity of each load to all

generators MVar output. !"_!" represents the sensitivity of each generator in MVar to

the marginal change of all loads. PLSGi and QLSGi represent the sensitivity of active

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Figure 3 –An example of generator’s active power losses as a function of produced reactive power at rated MW output

(Source: Staniulis, 2001)

Staniulis (2001) used the generator losses curve (figure 3) to estimate the losses, which is not seen in zonal pricing approach. Finally, the nodal reactive power price is presented in following formula:

!"#!" = !"!"∙! !!"# +!"#!"+!"#!" ∙!"!!!!!!!!!!!!!!!!!!!!!!!!!(6)

Where:

f(CQGi) – generator’s active power losses as a function of produced reactive power,

MW/MVar;

VSGi – generator’s voltage sensitivity, MVar;

SP – active power spot price.

Generator losses can be correctly allocated and remunerated under nodal pricing approach than zonal pricing approach. However, to calculate nodal price, it requires more information.

As mentioned, the distribution system is facing a huge challenge. A specific model for

distribution system was published by Haghighat & Kennedy (2010) in “A Model for

Reactive Power Pricing and Dispatch of Distributed Generation”. In this model,

Haghighat & Kennedy included renewable resources and load interruption. An important point is that the way of generating reactive power in renewable resources and in conventional resources may be different. Photovoltaic (PV) and Wind resource are the two most common renewable resources nowadays. PV panels generate direct current, and then a converter will convert it into alternating current. Therefore, Haghighat & Kennedy took this loss into account when calculating the payment. In the model, Haghighat & Kennedy broke down converter losses into two parts: a) switching losses and b) conduction losses.

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The converter losses are estimated through a second-order polynomial function as follows:

!"##_!" ! =!!_!+!_!∙!_!" +!_! ∙!_!"! _!!_!_!!!!!!!_!_!!!!!!!!!!_!_!_!_!!!_!_!!_!_!(7)

Where:

S is the apparent power output of the converter;

l0 is the coefficients of the loss curves denoting standby losses;

lV is voltage dependent losses;

lR is current dependent losses.

The receiving payment is also different for renewable resources. Usually, renewable resources are paid according to the feed-in-tariff (FIT), so Haghighat & Kennedy used FIT to calculate the cost. Moreover, Haghighat & Kennedy also took into account some other costs, such as capacity modification cost.

!_!"! !_!",!_!" = !"#_!" ∙Δ!"##_!" !_!",!_!" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!(8)! ! !!",!!" = !!"! !!",!!" +!!"! ∙!!"!"#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(9)

where:

FITPV is the feed-in tariff (FIT);

C0PV is per unit fixed cost that the PV plant will spend on converter size

modification;

QmaxPV is the maximum capacity of the converter.

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!!" !!" =!!"∙!!"+ !!"∙!!" ∙!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(10)

where:

aIL and bIL are coefficients that quantify the cost of un- served load;

ν_{IL is the customer willingness to interrupt its load from 0 to 1, which correspond to}

an extremely willing case and an unwilling case, respectively.

The customer willingness can help the estimation gets closer to the reality because each node may have different load flexibility.

2.3 Smart Grid

In this system evaluation, some new technologies are also introduced in

operating-side, such as smart meter and smart grid. Before these new technologies have been introduced into the power system, the power flow and information flow were unidirectional. The power flow is from producers to end-consumers and the information flow is from end-consumers to utility companies. However, after these new technologies have been introduced into the power system, the information flow becomes bidirectional. Smartening up the grid offers opportunities for changing the current energy markets, and this provides possibilities to develop new services and rearrange optimal network management (European Commission, 2014). In the smart grids environment, DSOs will be able to improve their services.

Smart grid can create and provide many new services and information, such as

flexibility services, energy efficiency services, and data handling. DSOs can use these services to improve their system management and service quality. In a smart grid environment, DSOs can better control grid information and demand-side information, due to employing the metering and communication equipment. These data have huge commercial value because it can be used to improve system quality, such as energy efficiency. DSOs can provide energy efficiency services to their consumers. This service can not only lower customers’ bills but also reduce their load consumption. Moreover, in table 2, it shows that information can help DSOs improve their congestion management by using flexibility services. Combining energy efficiency

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and flexibility services, DSOs can better adjust their infrastructure investment plans. In some circumstances, DSOs can even postpone their infrastructure investments.

Service Monopolistic characteristics Competitive characteristics

Public good

characteristics

Economies

of scale and

scope

Other externalities Incentives for

innovation Other Flexibility services Network and system management are public goods High economies of scale

Other characteristics of natural

monopoly (non-storability of

electricity, location rents, direct

connections to customers)

Large potential for

flexibility supply, ICT

allows for aggregation

of small flexible DER

Increasing number

flexibility providers,

limited number of

flexibility categories,

widely available price

information

Energy

efficiency

services

None Some

economies of

scale

Lack of awareness of benefits

and costs of energy efficiency,

negative externalities not

included in energy prices, split

incentives, high transaction costs

EPC projects

Limited entry and exit

barriers for technology

providers Data handling Non-rivalrous, (partly) non- excludable by legislation Substantial economies of scale

Lack of adequate guarantees on

privacy and use of smart meter

data, data security

Many suppliers and

users, market entry

may promote product

diversification

Low transaction costs

Table 2- Smart grid services (Source: European Commission, 2014)

However, even if smart grid and smart meter can help to improve system quality, they also create some new problems. In table 3, it summarizes some new challenges for liberalized energy market and DSOs.

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Service Key risks and issues in DSO market structure

Key risks and issues in liberalized market

structure

Flexibility services

·Inefficient allocation of flexibility between

DSOs and market actors

·Market based coordination not

technological feasible and economic

efficient in all types of distribution

networks

·Fragmented demand for flexibility lowers its

value

·Regulatory supervision required for

coordination

·Inefficient allocation of flexibility between

DSOs and TSOs

·More complex market structure lowers

understandability for non-experts

·Lack of information exchange between

DSOs and TSOs

·Concerns on market liquidity in case of

congestion

Data handling

·Competitive advantage for DSO by real-time

insights in network operation data combined

with ineffective unbundling

·Non-discriminatory third party access to

data not secured

·Lack of innovation incentives

·Too high number of DAMs, preventing

cost savings by realization of economies

of scale

· Data security risk

·Lack of simplicity and clarity for

consumers

Table 3- Smart grid issues (Source: European Commission, 2014)

2.4 Demand Response

According to European Commission, “demand response is to be understood as

voluntary changes by end-consumers of their usual electricity use patterns - in

response to market signals (such as time-variable electricity prices or incentive

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aggregation) to sell in organized energy electricity markets their will to change their

demand for electricity at a given point in time” (European Commission, 2013).

Because of smart meter and grid technologies, consumers are more involved in

changing of electricity prices. Depending on the regulation framework design, the

service providers can be divided into many different categories, such as load-serving

entities (LSEs), utility distribution companies (UDCs), electricity service providers

(ESPs), end-use consumers, load aggregators, and curtailment service providers

(CSPs) (Rahimi, Farrokh, & Ali Ipakchi, 2010).

One important value of DR is that it can help release government and utility

companies’ budget pressure during an economic down-term. To postpone an

investment plan is different from to delay an investment plan. The benefits for having

demand response are, including but not limited to, shifting the peak demand and

increasing service quality. There are also many different types of DR and different

pricing methodologies.

2.4.1 Contracted-based

In contracted-based program, there are direct load control and load interruption. For direct load control, consumers give an access and control right to their utility companies. For interruptible service, both parties will agree on a number of sheds (Palensky, Peter, & Dietmar Dietrich, 2011, 382). This contract will reward the consumer if he/she fulfills the requests. On the other hand, it may also incur a penalty if the consumer fails to respond.

2.4.2 Market-based

In market-based program, service providers submit their prices and the quantities to the market operator. Usually, the DR from residential level has to be aggregated and then be traded in the wholesale market.

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2.4.3 Real-time based (control by the price)

In real-time based program, there are time-of-user rates, critical peak pricing, and real-time pricing. These tools are similar to each other and the idea is offering a floating tariff to consumers. Consumers may schedule their consumption plans according to the floating tariff. By offering this tariff, utility companies or regulators are able to shift the demand and avoid some network constraints.

2.5 Operating methodologies

In order to adapt to the evolution, the operating method should also be upgraded. Traditionally, DSOs operate grids with radial structure. The power flow is

unidirectional, which is from the transmission substations to the end-users, and the consumption loads are with less flexibility. Under this condition, DSOs focus more on long term grid planning and design than on real-time operation (Knezovic, Codani, Perez & Marinelli, 2015). Therefore, when addressing voltage and congestion issues, DSOs usually will upgrade the cable transformers with the equivalent components that have higher rated power. Capacitor banks and transformers are the main tools to perform voltage regulation. The value of flexibility is non-existent under this kind of investment programs (“fit and forget” approach) (Knezovic et al, 2015). The situation is changing because the power and information flow is no longer unidirectional. Therefore, the value of flexibility has been created. The passive operating

methodology should also be transferred into an active control strategy. The active control strategies allow DSOs to better monitor and control the power injection and consumption. Therefore, some operating issues can be easily solved, such as line capacity congestions and voltage problems. Moreover, an active control allows DSOs to improve their service quality because DSOs are able to monitor and detect system issues in real-time. Active control strategies also help DSOs fulfill some energy policies, such as EU 20-20-20 (figure 4), because DSOs are able to provide extra services to increase energy efficiency and better integrate renewable resources.

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Figure 4 – EU 20-20-20 plan

(Source: Commission, DG Energy)

An active operating methodology was proposed by Y.He (2015) in “Demand

Response as an Active Source for Voltage Control of Distribution Networks with

Distributed Generations.” DR is introduced into the thermostatically controlled loads

(TCL). Based on the load temperature, the TCL will be switched on and off in respect to temperature limit and system commitment.

The evolution of internal temperature is presented as follows:

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where

is the ambient temperature;

= !!!!!!/!"!_{is the factor of inertia of the appliance;}_τ_{is the time step and mc is the}

thermal mass;

η is its coefficient of performance;

θk+1=ε⋅θk+

₍

1−ε

₎

⋅ θ0−ηXk⋅Pr A #

$

% &

' (+ωk

θ0

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A is the thermal conductivity;

is a noise process-modeling of the random external heat injections in

thermostatically controlled loads;

is a binary variable describing the ON/OFF operating state of TCL appliance at

period k.

The value of is controlled by a hysteric mechanism as follows.

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where !!is temperature

This TCL model is operating as a typical cooling appliance. The operation state !_! of

TCL k can be changed according to the TCL temperature !_!, which is shown as

follows.

Figure 5 - Operation state of TCL appliance

(Source: Y.He, 2015)

Moreover, a priority-stack-based control framework is applied that allows operators to better control and track TCLs state. There are several criteria that can be used to set up priority stacks, such as thermal cycle and working duration.

ωk k X k X ! " ! # $ = + 0 1 1 k k X X if if if min max min max θ θ θ θ θ θ θ < ≤ ≤ > k k k

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Figure 6 - Priority queue structure with TCL units

(Source: Y.He, 2015)

For the control process, the operator has to identify the amount of DR for each

TCL and how much should be used for each period (∆PDR). ∆PDR is obtained from

the optimization process in every 30 minutes. The operator will also need to know

how much DR can be used in real-time (∆Pact), which is between every 3 to 5 minutes.

If ∆PDR>∆Pact, some units in the OFF queue will be switched ON to fulfill the DR

action. If ∆PDR<∆Pact, some units in the ON queue will be switched OFF. After this

control process, the information of both queues should be updated, and it will be used for the next control period.

Figure 7 -TCL control processes

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Chapter 3 Methodology

Understanding the current situation and difficulties in the distribution system, there could be several options to adapt this evolution, and these options can be mixed because different situations may require different solutions. Presently, many countries are looking for a medium-term economic solution because of the current economic situation.

3.1 Distribution Generation

Using DG to perform the control voltage is an option because DG is closer to the demand than conventional generators. In order to reduce carbon dioxide (CO2) emission, many DG in Europe are also renewable resources, such as wind. Turitsyn (2011) demonstrated that under certain conditions, using DG could improve the system performance and power quality. However, DG voltage control performance will be limited by the line capacity and the converter capacity. In fact, in distribution system, an active power injection may create a bigger voltage fluctuation than a reactive power withdrawal because of the high R/X ratio. Consequently, to modify DG production can be another solution. However, modifying DG power output will create a revenue loss for the plant owner. Moreover, the marginal power production cost of renewable resource is zero, so modifying renewable power output can be the most expensive solution in term of production variable cost. Table 6 shows the wind power FIT in France.

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Table 4 - Cost of Wind in France

(Source: MINISTÈRE DE L'ÉCOLOGIE, DU DÉVELOPPEMENT DURABLE ET DE L'ÉNERGIE)

3.2 Demand Response

Before smart grid technology has been introduced into the distribution system, the communication cost is very high, so demand response is not economically feasible. After the technology has been introduced, the communication cost has been reduced and demand response becomes economically feasible. Using demand response to provide system services is also a trend in this evolution. Demand response can not only provide the system services but also improve energy efficiency. By shifting peak energy consumption, distribution network companies can postpone their grid reinforcement plans and consumers can save their bill at the same time. This is a win-win situation, especially when facing economic challenges. However, demand response is limited by many factors, such as type of loads, distance, and duration.

3.3 Grid reinforcement

In the traditional operating methodology, grid reinforcement is one method to address the congestion and voltage issues. However, it does not mean that grid reinforcement should not be considered in the active control methodology. Grid reinforcement actually can be the best solution during an economic booming period because the demand will increase constantly.

3.4 Model setting

In my paper, I apply a modified IEEE 34-node model to observe and calculate voltage profiles and the cost of voltage control in different scenario: a) using OLTC (base case), b) using OLTC and DG ancillary services, c) using OLTC, DG ancillary services, and DR, and d) usingOLTC, reactive power, and DR. Then, I compare each scenario result with the result of grid reinforcement.

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Figure 8 - Modified IEEE 34-node model

(Source: IEEE)

The checking period of this simulation is 30 minutes, and the market date starts from

1st of January 2014 to 31st of December 2014. The objective is to minimalize the

voltage control cost by using different resources in different scenario.

Min γ∗C1∗∆OLTC+C2∗∆PDG+C3∗∆QDG+C4∗∆PDR

where

γ is the DSO preference of using OLTC from 0 to 1, which correspond to an

extremely willing case and unwilling case, respectively;

C1 is cost of using OLTC;

C2 is cost of using DG;

C3 is price of reactive power;

C4 is cost of DR.

3.4.1 Cost of using OLTC

I assume that each year the maintenance cost is 0.5% of investment cost. According to

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Also, the OLTC can be switched up to 2200 times each year. Therefore, cost of using

OLTC is €22,085 (4,417,000*0.5%) divided by 2200, which is 10 €/ per switch.

3.4.2 Cost of using DG

In this simulation, the DG only offers downward reserve. In order to keep the system balance, the reducing amount will be compensated from the wholesale market. Therefore, I assume the cost of using DG equals to wholesale market price.

3.4.3 Cost of reactive power

DG can offer reactive power service to adjust the system voltage, but the value of service quality is difficult to estimate. Therefore, I use the sensitivity of the reactive power and the system losses to estimate the cost of reactive power because the system voltage and system losses have a positive relation. The coefficient of system losses of DG 1 reactive power is 0.015 MW/MVar, and the coefficient of system losses of DG 2 reactive power is 0.08 MW/MVar. The cost of reactive power is estimated by multiplying these coefficients with the market spot prices. The maximum reactive power output is 0.35*!_!"#.

3.4.4 Cost of DR

There are many different methods to estimate the value of DR. However, in my paper, I will use the French DR tariff as shown in Figure 9.

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Figure 9 – Demand Response prices and hours

(Source: RTE)

In this simulation, the DR is offering both upward and downward reserves, and for each bus, the amount of DR is 30% of the bus consumption.

In order to gradually introduce ancillary services into distribution network, I use multiple OLTC costs to present DSO’s preference. This preference will influence the voltage control profile. The cost of each resource is also presented with the weight, and C2, C3, and C4 are derived from the market result, which cannot really be modified. In general, DSOs do not want to frequently adjust OLTC. I assume that after introducing ancillary services into the voltage control, DSOs are willing to adjust OLTC twice per day if possible. Therefore, in figure 10, I assign three different values

for γ: 0.01, 0.55,and 1. The two lower costs present the DSO’s preference. In the

total cost calculation, the first two switches still cost 10 euros. These different costs also help to solve the conflict between local and global optimization because the effect of OLTC in voltage control is different than other resources.

Figure 10 – DSO preference 0!

0.2! 0.4! 0.6! 0.8! 1! 1.2!

1! 2! 3! 4! 5!

Value

Switches

DSO/preference/

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Chapter 4 Results

4.1 Base case: OLTC

In the base case, DSOs cannot control reactive power, DG and DR. Figure 11 shows the load and voltage profile in the system.

Figure 11 –Load profile and based case voltage profile

There are a total of 604,800 (35*48*360) checkpoints in this voltage figure. The

overvoltage violations are 108 times and the low voltage violations are 979 times, so

the violation rate is 0.18%. Moreover, figure 11 also shows that the voltage violations mainly happen in the first quarter and fourth quarter due to the heavy demand. During the winter and early spring, the heavy heating demand triggers huge electricity

consumption.

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In bus 35, it connects with a 4.4 MW wind farm. Since bus 35 is far from the consumption area, the wind farm creates some overvoltage events. One violation (30 minutes in total) in one day happens 30 times during a year, two violations (60 minutes in total) in one day happens 13 times, three violations (90 minutes in total) in one day happens 7 times, four violations (120 minutes in total) in one day happens 5 times, five violations (150 minutes in total) in one day happens 1 time, seven violations (210 minutes in total) in one day happens 2 times, and eight violations in one day happens 1 time.

Figure 13- Bus 23 voltage profile

In bus 23, it connects with another 3.2 MW wind farm. Unlike bus 53, bus 23 is closer to the consumption area. Therefore, this wind farm helps improve the voltage in this area, but sometimes this area still has low voltage problems. One violation in one day happens 15 times during a year, two violations in one day happens 8 times, three violations in one day happens 1 time, and four violations in one day happens 1 time.

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Figure 14 – Bus 34 voltage profile

Bus 34 locates at the end of the feeder, so it suffers many low voltage violations. One violation in one day happens 24 times during a year, two violations in one day happens 16 times, three violations in one day happens 10 times, four violations in one day happens 4 times, and five violations in one day happens 4 times.

Figure 15 – Bus 34 voltage profile

Unlike bus 34, bus 15 locates in the middle of the feeder, so it doesn’t suffer any voltage violation. Moreover, unlike bus 35, bus 15 does not have DG connection and bus 15 is also far from the connecting point, so it does not have overvoltage violation.

The base case shows that DG can help to improve the voltage quality when it connects with a consumption area. Moreover, only using OLTC to perform a voltage control, the effect in the second part of the feeder is limited. The total OLTC switching times is 1897.

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4.2 Case 1: OLTC& DG ancillary services

In case 1, DSOs can use not only OLTC but also DG ancillary services from DG. Figure 16 shows the improved voltage profile and the cost of this optimization. The total cost of this optimization is 11,778.02 euros.

Figure 16 – Case 1 voltage profile and cost

Figure 17– Case 1 bus 35 voltage profile

Figure 17 shows that the voltage quality of bus 35 has improved. The total amount of curtailment for DG1 in this optimization is 17.8MWh.

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Figure 18 – Case 1 bus 23 voltage profile

Unlike bus 35, bus 23 used to have low voltage problems. After this optimization, there are no more low voltage violations. The amount of curtailment for DG 2 is far lesser than DG 1 because bus 23 used to have low voltage events. The amount of curtailment for DG2 is almost zero MWh.

After using OLTC and DG ancillary services, DSOs can eliminate all the voltage violations. Moreover, the OLTC switching time is reduced. As mentioned, the OLTC switching time has a negative relationship with its useful life. The switching time reduces from 1897 to 989.

4.3 Case 2: OLTC, DG ancillary service, and DR

In this case, DSOs can use OLTC, DR and ancillary service without environmental constraint. I assume that there is a DR aggregator in each zone and DSOs can use this aggregator to control the zonal DR. According to the voltage sensitivity, there are four DR zones in this system: zone 1 (1~6 buses), zone 2(7~15buses), zone 3(16~23buses), and zone 4 (24~34 buses). Figure 19 shows the improved voltage profile and the cost of this optimization. The total cost of this optimization is 11,323.19 euros.

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Figure 19 – Case 2 voltage profile and cost

The voltage quality of bus 35 has improved. The total amount of curtailment for DG1 in this optimization is 14.83 MWh.

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The voltage quality of bus 23 also has improved. The amount of curtailment for DG2 is also almost zero MWh.

After adding DR into the control system, the control cost has been reduced. The amount of curtailment for DG1 also has been reduced. Instead of frequently changing OLTC, DSOs now can adjust DR and reactive power to solve some short-term voltage violations. The OLTC switching time reduces from 989 (in Case 1) to 947.

4.4 Case 3: OLTC, DR, and ancillary service

In this case, DSOs can also use OLTC, DR and ancillary service, but the DG curtailment should be minimized due to environment constraints. Figure 22 shows the improved voltage profile and the cost of this optimization. The total cost of this optimization is 11,509.53 euros.

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The voltage quality of bus 35 has improved. The total amount of curtailment for DG1 in this optimization is 1.534E-14 MWh.

The voltage quality of bus 23 also has improved. The amount of curtailment for DG2 is 5.0569E-15 MWh.

Comparing to Case 2, Case 3 has a higher OLTC switching time. The switching time increases from 947 times to 1067. Because of the environmental constraints, DSOs have frequently adjusted the OLTC to maintain the voltage quality.

4.5 Case 4: Grid reinforcement

In this case, DSOs will replace all its overhead lines with underground cables. Table 5 shows the system figure.

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Node A Node B Distance (km) Type Node A Node B Distance (km) Type

1 2 0.790 Underground 25 30 0.620 Overhead

7 8 0.800 Overhead 28 29 0.160 Overhead

20 21 0.250 Overhead 45.905

Table 5 – Lines information

(Source: Yujun, 2015)

I assume that there are two investment plans: 3-year plan and 5-year plan. Moreover, in both plans, there are two scenarios: high cost and low cost. The total length that will have to replace is 39.765 kilometer (Km).

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Figure 25 – Case 4 voltage profile

After the replacement, there is no more voltage violation. Currently, the annual interest rate is around 1.25%, so the monthly interest rate is 0.104% (1.25% / 12). Moreover, I assume that the utility company has to pay its labor and material cost monthly. Therefore, in order to have enough money for each payment, the utility company has to deposit an amount of money in its bank account. I use present value interest factor of annuity (PVIFA) to estimate the amount of deposit.

Table 6 – Cost of grid reinforcement

(Source: L’APPORT DE NOUVELLES TECHNOLOGIES DANS

L’ENFOUISSEMENT DES LIGNES ÉLECTRIQUES À HAUTE ET TRÈS HAUTE

TENSION, Christian KERT)

The construction cost can be very different due to many different factors, such as labor cost and the replacement length. In order to estimate a fair cost, I use the price list, issued by the French government in 2000. For medium voltage (15~20 KV), the

total cost of installing underground cable is between 50,000 to 150,000 €/ Km

3-year plan (36 months) with high cost:

The total amount have to invest is 5,964,750 euros (150,000∗39.765), so the monthly

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Table 7 – 3-year plan with high cost

3-year plan (36 months) with low cost:

payment is around 66,275 euros (2,385,900/36).

Table 8 – 3-year plan with low cost

5-year plan (60 months) with high cost:

Table 9 - 5-year plan with high cost

5-year plan (60 months) with low cost:

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4.6 Economic analysis

All the case results show that DSOs can always solve the voltage violations in base case. The cost of voltage control depends on the regulation policies and market structure. However, the next challenge is what if the demand keeps increasing? Are DSOs still able to solve all the violations? In the following analysis, I am going to increase the demand and to observe the result.

Figure 26 – Voltage violations

I assume that each year the total demand will increase 1%. Figure 26 shows that for using OLTC and DG ancillary services (Case 1), its number of voltage violations will be higher than what the base case has after 11 years. For using OLTC, DG ancillary services, and DR (Case 2), its number of voltage violations will be higher than what the base case has after 23 years. For using OLTC, reactive power and DR (Case 3), its number of voltage violations will be higher than what the base case has after around 19 years. For grid replacement, the number of voltage violations will be higher than what the base case has after 60 years.

0! 200! 400! 600! 800! 1000! 1200! 1400! V ol ta ge /v io la ti on s Demand/growth/ Case!1! Case!2! Case!3! Reinforement!

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Figure 27 – Cost comparison 1

The cost of each method is very different. Figure 27 shows the cost comparison of Case 2 and grid reinforcement (5-year, low cost) in each year. The cost of voltage control in grid reinforcement is calculated through the straight-line method. For each year, I divide the replacement cost by 60 years. As the figure 27 shows, after 20 years, the voltage cost of Case 2 gets higher than grid reinforcement. The total cost of Case 2 for 23 years is 547,813.91 euros and the total cost of grid reinforcement for 23 years is 802,868.67 euros.

Figure 28 – Cost comparison 2 0!

10000! 20000! 30000! 40000! 50000!

1%! 2%! 3%! 4%! 5%! 6%! 7%! 8%! 9%! _10%! _11%! _12%! _13%! _14%! _15%! _16%! _17%! _18%! _19%! _20%! _21%! _22%! _23%!

Eu

ro

s/

Demand/growth

Total/cost/

Case!2! Reinforement(5@year,!L)!

0.00! 10000.00! 20000.00! 30000.00! 40000.00!

1%! 2%! 3%! 4%! 5%! 6%! 7%! 8%! 9%! _10%! _11%! _12%! _13%! _14%! _15%! _16%! _17%! _18%! _19%!

Eu

ro

s

Demand/growth

Total/cost

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Figure 28 shows the cost comparison of Case 3 and grid reinforcement in each year. The cost of grid reinforcement is always higher than the voltage control cost of Case 3. The total cost of case 3 for 19 years is 398,725.99 euros and the total cost of grid reinforcement for 19 years is 663,239.33 euros.

If I change DSO preference from {0.01,0.55,1} to {0.25, 0.6,1}, the effect result remains the same because DSO preference will only effect the usage of each resource.

Figure 29 – preference comparison

Figure 30 – Cost comparison 3 0! 200! 400! 600! 800! 1000! 1200! 1400!

1! 2! 3! 4! 5! 6! 7! 8! 9!10!11!12!13!14!15!16!17!18!19!20!21!22!23!

V ol ta ge /V io la ti on s Demand/growth Case!1! Case!1@1! Case!2! Case!2@1! Case!3! Case!3@1! 0.00! 5000.00! 10000.00! 15000.00! 20000.00! 25000.00! 30000.00! 35000.00! 40000.00! 45000.00! Eu ro s Demand/growth Case!2! Case!2@1!

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Figure 31 – Cost comparison 4 0!

5000! 10000! 15000! 20000! 25000! 30000! 35000!

1%! 2%! 3%! 4%! 5%! 6%! 7%! 8%! 9%! _10%! _11%! _12%! _13%! _14%! _15%! _16%! _17%! _18%! _19%!

Eu

ro

s

Demand/growth

Case!3!

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Chapter 5 Conclusion

Facing the new type of load and technologies, the operating system should be improved. Because of the smart meter and smart grid technologies, DR and ancillary services in distribution system become economic feasible. The operating strategies should be changed from passive control into active control because the value of flexibility has been created. Active control not only improves the system quality but also creates some extra services. The transmission experience cannot really apply in distribution system because of the difference in types of generation, line features, and grid topology.

DSOs should take advantage of the new technologies and load flexibility. The Case 1 result shows that using DG ancillary services can help to postpone the system reinforcement for 11 years. The Case 2 result shows that combining with DR, the reinforcement plan can be postponed for 23 years, which is twice longer than without using DR. Like electricity, DR cannot be stored in a large scale, so either use it or lose it. Therefore, DSOs should really consider using this resource.

Regulation policies also play an important role in system control. As Case 3 result shows, if DG output cannot be modified, the system reinforcement plan cannot be further postponed comparing to Case 2. However, after all, the system reinforcement cannot be avoided if the demand keeps growing.

In current situation, the interest rate is significant low, so it only plays a small effect on the investment plan. On the other hand, the length of the investment plays a more important role on the investment. However, if the interest increased to 5.25%, it can help to reduce the actual investment cost up to 12%.

In the system control, DSO’s preference helps gradually introduce ancillary services into distribution system because the usage of each resource is changed according to the preference. If the DSO wants to use more ancillary services, such as DR and DG, to perform voltage control, it can increase the “value” of using OLTC. Therefore, the

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usage of other resources will increase. The DSO preference will only affect the control cost because the total amount of each resource has not changed. Therefore, the total cost can be further reduced when DSOs believe ancillary services and DR are reliable. This will make grid reinforcement even less attractable. Again, the future remains the same, so there is no way to avoid grid reinforcement if the demand keeps growing.

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a hierarchical voltage control." Energy Market (EEM), 2010 7th International

Conference on the European. IEEE, 2010.

Staniulis, Robertas. "Reactive power valuation." Lutedx/(TEIE-5150)/1-42(2001).

Haghighat, H., and S. Kennedy. "A model for reactive power pricing and dispatch of

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IEEE, 2010.

Rahimi, Farrokh, and Ali Ipakchi. "Demand response as a market resource under the smart grid paradigm." Smart Grid, IEEE Transactions on 1.1 (2010): 82-88.

Turitsyn, Konstantin, et al. "Options for control of reactive power by distributed photovoltaic generators." Proceedings of the IEEE 99.6 (2011): 1063-1073.

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Services and Flexibility Provision by Electric Vehicles': a Review of Options." In

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Yujun He and Marc Petit. "Demand Response as an Active Source for Voltage Control of Distribution Networks with Distributed Generations" Group of Electrical Engineering Paris (GeePs), UMR CNRS 8507, CentraleSupelec, UPSud, UPMC, (submitted, non published)

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Appendix A

Market spot price

€/MWh 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Wed, 01/01 15.2 13.0 12.1 11.7 11.7 11.4 9.9 9.5 9.5 11.6 11.9 13.2 15.2 13.7 12 10 12 15 16 18 16 14 15 13

Thu, 01/02 9.6 7.6 5.0 0.1 1.1 7.1 12.5 21.3 30.4 35.5 33.1 33.8 38.0 37.4 36 32 34 53 67 54 40 36 35 31

Fri, 01/03 27.4 25.2 15.6 8.7 11.3 12.3 26.0 31.7 32.0 31.9 31.0 31.5 39.1 31.0 30 30 31 37 35 42 30 26 32 32

Sat, 01/04 11.9 10.5 7.9 5.2 4.9 9.0 8.7 9.9 11.5 12.8 13.4 14.0 15.6 14.2 14 17 13 17 21 18 16 14 15 17

Sun, 01/05 15.5 14.7 13.3 11.0 9.8 11.7 11.0 11.4 13.8 27.4 30.9 32.5 32.1 29.9 28 17 15 35 40 38 35 29 29 22

Mon, 01/06 13.8 11.9 9.9 5.1 3.8 8.2 17.3 48.6 46.6 40.0 40.1 39.7 40.0 37.9 35 32 31 43 55 51 42 28 39 34

Tue, 01/07 9.3 10.0 3.9 0.1 2.1 6.5 26.1 32.3 49.4 52.0 52.0 54.4 52.8 50.0 46 43 46 54 62 56 40 32 36 34

Wed, 01/08 22.0 14.6 12.7 11.3 10.0 22.4 30.3 46.4 58.0 57.8 53.7 54.5 56.5 54.3 51 45 47 58 65 62 48 39 40 39

Thu, 01/09 27.2 26.5 24.8 18.3 13.0 25.0 34.7 48.0 57.0 48.5 47.0 47.4 48.9 46.7 42 38 44 53 62 60 48 41 45 44

Fri, 01/10 42.6 38.0 32.2 16.3 15.5 33.8 46.7 62.9 59.5 61.6 60.0 58.3 57.7 53.8 51 47 50 60 66 62 57 47 50 47

Sat, 01/11 40.4 28.2 35.0 28.3 26.8 28.3 34.1 38.3 43.7 45.0 46.4 46.3 49.7 41.9 38 38 40 52 59 59 51 45 53 49

Sun, 01/12 43.5 40.0 25.9 17.0 14.5 16.5 16.2 23.1 31.5 35.7 25.8 24.0 29.7 24.7 26 27 31 40 42 46 37 33 38 32

Mon, 01/13 26.0 27.9 27.6 13.5 14.2 26.7 33.1 50.8 51.5 53.9 56.1 56.8 55.9 51.8 48 49 58 63 64 61 52 43 43 39

Tue, 01/14 31.1 29.7 29.6 24.2 19.7 30.3 37.0 60.1 65.9 66.1 67.0 67.5 60.0 55.0 53 52 56 71 68 54 55 45 45 40

Wed, 01/15 33.0 30.7 29.9 29.6 29.5 30.7 39.9 55.7 62.7 58.1 55.5 53.9 54.2 54.4 51 51 52 56 63 61 47 39 39 36

Thu, 01/16 30.1 28.9 25.6 21.4 18.4 28.7 33.4 50.1 48.3 51.6 50.8 52.2 51.5 51.5 50 48 47 50 56 55 46 35 38 37

Fri, 01/17 29.5 28.2 19.6 11.2 11.2 20.7 34.0 49.0 50.0 47.7 47.9 48.0 48.7 46.2 42 41 42 49 53 49 44 33 34 36

Sat, 01/18 30.5 29.8 28.6 26.8 18.6 22.3 22.0 30.3 33.3 40.0 35.2 32.4 31.3 30.9 31 31 33 40 45 40 30 29 30 39

Sun, 01/19 36.1 30.1 26.2 9.5 12.8 16.4 12.2 15.8 30.0 37.6 44.4 46.5 50.0 44.1 36 27 30 40 45 47 43 40 42 38

Mon, 01/20 34.8 29.3 22.2 14.0 13.1 25.5 45.9 72.0 70.9 64.5 62.9 64.4 59.6 58.0 54 50 53 65 78 64 63 50 58 49

Tue, 01/21 44.8 34.4 30.7 30.3 30.5 33.7 45.9 59.9 63.0 60.2 63.3 65.7 62.9 61.5 57 51 54 60 61 63 53 48 51 47

Wed, 01/22 45.7 43.1 35.0 31.0 31.1 35.4 48.5 67.5 66.5 65.7 60.9 62.8 61.4 59.4 59 55 62 72 80 64 62 54 62 54

Thu, 01/23 41.8 41.5 39.2 31.3 31.2 34.0 43.1 60.6 65.1 65.1 64.9 62.2 60.9 60.9 55 50 48 55 64 58 54 45 54 47

Fri, 01/24 35.1 32.3 30.3 30.0 30.5 32.2 43.4 61.6 62.5 63.3 61.6 63.3 60.4 59.3 59 53 53 64 65 64 55 50 47 49

Sat, 01/25 37.7 32.1 31.1 30.3 29.8 29.0 30.9 31.6 39.3 42.0 43.6 44.1 45.8 37.7 33 33 34 38 48 43 33 30 33 38

Sun, 01/26 22.1 19.1 14.9 13.1 13.2 12.7 9.5 14.1 14.0 22.2 22.7 22.9 23.4 19.1 15 13 8 18 22 27 32 24 28 20

Mon, 01/27 12.6 11.7 12.8 7.1 8.8 13.1 30.1 47.4 51.1 52.5 53.5 52.7 56.1 50.7 52 52 51 56 80 64 47 39 40 39

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Wed, 01/29 38.7 30.5 29.6 29.0 29.6 31.1 37.1 55.4 53.0 52.9 57.4 56.8 53.6 54.0 50 47 47 62 83 73 54 50 54 52

Thu, 01/30 37.8 34.9 34.3 29.9 30.3 34.4 45.2 53.1 54.7 64.8 60.0 64.2 59.7 54.5 52 52 52 55 68 60 51 46 47 47

Fri, 01/31 43.0 42.5 36.5 33.1 32.0 40.0 46.9 69.9 72.0 72.2 65.9 60.9 52.9 48.1 45 44 44 53 62 56 49 40 42 39

Sat, 02/01 31.0 28.9 26.6 20.9 20.2 20.7 26.8 28.7 37.3 42.7 43.3 44.6 48.6 40.2 33 33 33 44 50 45 41 36 35 36

Sun, 02/02 41.6 32.0 25.8 19.4 13.2 14.1 16.5 18.9 22.1 30.8 32.0 31.8 34.2 32.1 31 31 33 36 49 55 54 46 50 49

Mon, 02/03 44.4 37.8 36.0 31.6 31.5 36.2 54.1 71.9 72.9 67.5 57.2 54.6 52.9 52.0 47 47 47 54 68 60 58 49 52 52

Tue, 02/04 44.4 45.0 40.9 30.6 30.0 32.4 47.1 60.3 58.5 53.9 52.0 52.8 54.7 51.7 48 48 48 53 64 56 48 41 44 42

Wed, 02/05 30.5 30.0 29.0 25.7 18.1 28.1 33.5 45.2 49.9 52.6 58.6 54.2 48.1 52.2 50 44 43 50 67 53 37 57 52 45

Thu, 02/06 42.3 39.9 34.8 28.3 28.7 32.2 44.0 55.9 56.7 58.8 61.8 60.4 57.3 55.9 55 50 48 56 66 60 48 37 34 40

Fri, 02/07 23.6 19.5 14.7 12.2 8.5 15.4 30.7 47.8 45.7 47.6 47.9 51.3 48.4 42.9 37 32 31 36 60 55 43 30 38 41

Sat, 02/08 28.0 26.4 25.9 24.9 10.5 16.2 24.0 27.1 29.5 29.5 28.1 26.8 28.0 25.5 26 29 28 31 43 34 28 24 28 24

Sun, 02/09 14.2 13.0 12.9 11.8 9.7 9.4 10.6 10.5 11.0 19.2 17.7 17.3 14.7 13.2 11 9 12 15 36 37 31 28 30 25

Mon, 02/10 36.1 33.9 27.2 23.9 23.1 33.2 45.4 59.4 61.0 58.8 60.0 55.0 56.1 56.8 56 51 47 55 79 54 50 47 48 43

Tue, 02/11 30.8 32.1 29.5 28.3 28.1 30.7 41.1 53.8 55.3 56.6 54.1 51.7 50.4 49.3 42 40 41 52 59 67 50 46 49 44

Wed, 02/12 45.0 41.9 37.8 28.4 29.4 36.7 45.5 59.3 65.8 68.4 60.9 55.9 50.3 49.4 46 43 41 45 59 54 52 43 46 44

Thu, 02/13 43.0 34.5 32.2 18.3 12.5 26.7 42.4 55.9 53.5 57.8 56.7 58.0 55.0 52.9 52 45 43 49 69 59 53 42 41 38

Fri, 02/14 33.0 32.7 29.3 24.4 25.6 29.4 46.4 61.1 64.8 69.3 62.1 55.0 52.1 47.1 44 36 40 46 53 49 37 30 31 42

Sat, 02/15 27.7 18.0 12.4 10.4 10.1 10.3 11.4 13.3 18.3 22.7 23.1 23.1 23.8 22.5 21 19 20 28 39 45 29 29 42 42

Sun, 02/16 25.5 14.5 12.4 9.1 5.3 8.1 11.1 9.5 10.7 13.4 16.8 17.9 18.2 13.2 11 10 12 15 40 48 47 35 39 32

Mon, 02/17 31.6 25.7 23.3 17.5 19.6 26.5 43.8 58.8 53.3 54.0 49.3 50.0 44.2 42.1 35 37 40 43 82 72 57 47 50 43

Tue, 02/18 32.0 31.7 30.1 28.9 29.2 31.3 42.0 56.2 54.9 53.8 51.9 50.7 51.4 48.5 43 43 46 54 74 60 46 40 42 36

Wed, 02/19 32.2 29.7 28.5 27.7 28.5 29.3 38.2 47.5 49.4 52.2 53.9 54.0 50.8 49.5 49 48 45 47 70 60 54 47 44 45

Thu, 02/20 31.3 29.5 28.9 27.8 25.6 27.9 34.5 46.3 48.3 48.3 44.9 47.0 47.6 44.9 40 35 32 41 55 52 47 40 42 41

Fri, 02/21 32.9 22.2 20.8 19.4 21.0 26.6 35.8 46.3 49.0 53.0 50.1 48.5 42.9 37.6 32 32 32 43 49 50 49 41 41 41

Sat, 02/22 35.1 30.0 26.1 21.0 18.7 21.2 27.9 29.4 32.9 37.4 37.4 36.9 38.9 35.5 30 32 31 38 51 53 44 37 40 37

Sun, 02/23 26.1 21.6 22.1 19.5 16.3 19.9 15.7 15.7 17.1 16.6 17.5 16.8 14.7 13.0 11 7 11 11 24 35 28 23 27 26

Mon, 02/24 14.5 15.1 17.2 13.7 14.0 18.1 35.7 47.0 50.0 46.7 46.0 41.8 40.5 39.3 36 31 33 46 65 65 49 35 37 34

Tue, 02/25 26.2 23.9 22.8 20.3 19.0 25.9 37.0 47.0 46.7 46.1 44.6 44.0 44.9 40.5 36 35 34 43 73 63 47 40 43 40

Wed, 02/26 36.1 30.0 27.3 26.9 27.9 28.5 39.2 45.1 49.2 51.3 50.4 50.0 46.9 46.4 45 43 42 44 71 73 50 46 42 40

Thu, 02/27 34.0 32.0 30.3 29.6 29.5 32.2 41.5 53.3 50.1 47.1 48.1 46.0 44.2 44.8 43 42 41 52 65 58 49 43 41 40

Fri, 02/28 36.3 34.9 30.2 28.0 28.5 29.9 39.6 47.5 49.5 49.8 49.1 47.4 46.7 44.7 42 42 43 47 65 60 47 40 43 42